Abstract

We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.

(Color online) Periodically poled PhC structure. The red portions correspond to the original orientation of the nonlinear crystal when χ(2) is positive, while in the blue portions, the crystal’s orientation is flipped resulting in a negative χ(2).

(Color online) CMT calculations: (a) Color contour plot of the unnormalized terahertz energy density ε(x,y)|E(x,y,t)|2 at t=1010(a/c), in a 2D box of size 1a×80a. (b) A zoom-in version of the plot in Fig. a, showing more details of the interval y∈±[8a,19a]. Note that the optical beam was originally sent through the waveguide at y=0

(Color online) FDTD calculations: (a) Color contour plot of the terahertz energy density ε(x,y)|E(x,y,t)|2 at t=1010(a/c), in a 2D box of size 1a×80a. (b) A zoom-in version of the plot in Fig. a, showing more details of the interval y∈±[8a,19a]. Note that the optical beam was originally sent through the waveguide at y=0.